## Upcoming Talks

### March 27, 2019

#### A Mathematicians Guide to Finance - How I stopped worrying and learned to love financial economics

Mathematical Finance typically is not overly concerned with standard finance theory or economics generally. Rather, practitioners and academics usually focus on modelling an endogenous process (e.g. a stock price) apply a simple modelling assumption (e.g. no arbitrage) and derive formulae useful for valuation (e.g. the Black-Scholes-Merton equation). Along with studies in the actuarial sciences this is often the extent of mathematicians interaction with finance. In this talk we will explore a stylized history of modern financial economics and the relevant mathematical problems that arise in fiance and insurance with some discussion of open problems of interest.

## Past Talks

### March 20, 2019

#### Almost Disjoint Families and Topology

We will discuss some work of Michael Hrusak on almost disjoint families. We will prove a frew of the results in this paper with a small introduction to Luzin families. The talk will end with starting some interesting open problems which remain in this area.

### November 26, 2018

#### On Efimov's Problem

Every topological space is infinite and Hausdorff (just while you read this, of course)

Question 1: Does Every compact space contain an infinite convergent sequence?

To see why the answer to Question 1 is surprisingly negative, we will talk about compactifications and just a little bit about ultrafilters. In fact $\beta\mathbb{N}$ the Stone-Çech compactifcations of the integers (or the set of ultrafilters over $\mathbb{N}$) is a counterexample.

Efimov's Problem asks whether $\beta\mathbb{N}$ is the counterexample to Question 1; that is:

Question 2 (a.k.a. Efimov's Problem): Does every compact space contain either:

• An infinite convergent sequence.

### October 5, 2017

#### Title: Artificial Intelligence and Analysis of Non-stationary Spatial-temporal Data

In this talk, I will first give a brief introduction to the area of Artificial Intelligence (AI) in which the main differences between Strong AI and Weak AI, and some of the mathematical as well as philosophical theories formulated for describing each of these subareas will be discussed. I will further review the advances in Machine Learning research and current state-of-the-art in Deep Learning, Statistical Learning and Tensor Decomposition-based Learning methods. The rest of the talk will focus on the main challenges and difficulties confronted when analyzing the non-stationary spatial-temporal data using the machine learning approach. As a real-world example of such a complex data, electroencephalogram recordings of patients having major depressive disorder will be demonstrated on which I will share some of my recent research achievements. Our proposed framework utilized for analyzing the mentioned data involves the use of various techniques developed in statistics, operations research, machine learning and big data

### September 28, 2017

#### Change-point detection for noisy non-stationary biological signals

Experimentally and clinically collected time series data are often contaminated with significant confounding noise, creating short, non-stationary time series. This noise, due to natural variability and measurement error, poses a challenge to conventional change point detection methods. We proposed a novel, real-time change point detection method for effectively extracting important time points in non-stationary, noisy time series. We validated our approach with three simulated time series, as well as with a physiological data set of simulated labour experiments in fetal sheep. Our methodology allows for the first time the detection of fetal acidemia from changes in the fetus' heart rate variability, rather than traditional invasive methods. We believe that our method demonstrates a first step towards the development of effective, non-invasive real time monitoring during labour from signals which may be easily collected.

### September 21, 2017

#### Kick-off Problem Session

This week we are having audience members introduce a problem they are interested in studying. Each person will take only 5 minutes to give the problem statement and some of the tools used. This session will act as a preview for what may appear in the upcoming weeks. Afterward we will try to fill up the time slots with volunteer speakers.